The system of conservation laws \( (\ref {nstuidao2}) \)  with \( (\ref {Riemanchuzhi}) \)  has three distinct real eigenvalues (see Ref. [1]})
\(\lambda _1 = -\sqrt{\frac{\gamma p}{v}} < 0,\qquad \lambda _2 = 0, \qquad \lambda _3 = \sqrt{\frac{\gamma p}{v}} > 0,\) 
